Question
Download Solution PDFIn the figure, O is the centre of the circle. If \(\angle ARS = 125^\circ,\) then find the measure of \(\angle PAB.\)
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
\(∠ ARS = 125^\circ\)
Concept:
Angle made in a semi-circle is a right angle.
Angles formed in the same segment of a circle will be equal in measure.
Calculation:
BR is formed by joining B and R.
∠ARS + ∠ARP = 180° [Linear Pair]
⇒ ∠ARP = 180° - 125° = 55°
∠ARB = 90° [Angle made in semi-circle]
⇒ ∠ARP + ∠BRP = 90°
⇒ ∠BRP = 90° - 55° = 35°
∠BRP = ∠PAB = 35° [Angles made in the same segement]
∴ ∠PAB = 35°
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